Alfred Centauri

*Consciousness is an axiomatic concept which means that it is self-evident and cannot be analyzed. From ITOE: An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest. ... The first and primary axiomatic concepts are “existence,” “identity” (which is a corollary of “existence”) and “consciousness.” One can study what exists and how consciousness functions; but one cannot analyze (or “prove”) existence as such, or consciousness as such. These are irreducible primaries. (An attempt to “prove” them is self-contradictory: it is an attempt to “prove” existence by means of non-existence, and consciousness by means of unconsciousness.) **Objectivism rejects the analytic/synthetic distinction. From ITOE: The Objectivist theory of concepts undercuts the theory of the analytic-synthetic dichotomy at its root. . . . Since a concept is an integration of units, it has no content or meaning apart from its units. The meaning of a concept consists of the units—the existents—which it integrates, including all the characteristics of these units.

Have a look at: http://objectivistanswers.com/

From "Ayn Rand Answers" page 4: Do severely retarded individuals have rights? Not actual rights - not the same rights possessed by normal individuals. In effect, they have the right to be protected as perennial children. ... But you could not extend the actual exercise of individual rights to a retarded person, because he's unable to function rationally. Since all rights rest on human nature, a being that cannot exercise his rights cannot have full human rights."

Here's something off the top of my head: First, recall that "A “right” is a moral principle defining and sanctioning a man’s freedom of action in a social context." Second, recall that "the right to life means the right to engage in self-sustaining and self-generated action—which means: the freedom to take all the actions required by the nature of a rational being for the support, the furtherance, the fulfillment and the enjoyment of his own life. (Such is the meaning of the right to life, liberty and the pursuit of happiness.)" Finally, recall that only humans have a choice to live - plants and lower animals act more or less automatically. It is this fact - man's nature as a volitional being - that is the source of his right to life.

According to Penrose and his Conformal Cyclic Cosmology, there is a way to identify the heat "death" of this "aeon" with the minimum entropy "big bang" of the next. On such a view, the Universe is indeed eternal with the "initial singularity" of the current aeon identified as the maximally decayed state of the previous.

bluearmy wrote: From "Ayn Rand Answers", pg. 149 Bottom line, if you are a theist, you are not an Objectivist. You may agree with much of Objectivism and even live Objectivist "like" but, to quote Ayn Rand, "the contradictions are yours".

Don't forget that, within Objectivism, definitions are either true or false. As I understand things, within Objectivism, one cannot construct a true definition of a system of ethics out of context, i.e., without specifying why man needs a code of values.

Let me re-quote the comment I replied to: First of all, without government, there is no legal system so isn't it almost trivial to say that there are no legally enforceable claims without government? If this is what the author meant, then I agree but so what? Still isn't it true that, in the absence of government, one may elect to enforce his individual rights, e.g., his right to produce and to keep the fruits of his production, himself or elect to trade with others to enforce them for him and that it is right for him to do this?

Your reply seems trivial and irrelevant. Even under the rule of objective law, a gang of thugs remains a gang of thugs. Telling them that the government will retaliate against them is as unlikely to dissuade them as telling them about inalienable rights so what exactly is your point?

I disagree. Government is not the source of rights. Men possess objective, inalienable rights because of their nature as rational beings. These rights can, and most likely will, be violated without the rule of objective law to protect them but these rights do not evaporate when there is no government.

I'm not convinced that the notion of a particle that includes wave-like properties is coherent. Also, the classical notion of "particle" (an entity with definite spatial localization) survives in Bohmian Mechanics so one does not have to accept the notion of a particle with wave-like properties to get predictions that correspond with experimental results. Rather, one must instead accept explicit non-locality.

For particle physicists, the word "particle" labels a vastly different concept than the classical concept "particle". For example, in the context of Quantum Field Theory, a particle is an elementary excitation of an underlying quantum field. Within QED, the photon has definite energy. To have definite energy, a photon is localized in momentum space but not position space. In classical physics, a particle is localized in both position space and momentum space. But in quantum mechanics and quantum field theory, there is no particle state that is localized in both spaces (although there are states that minimize the product of the "spreads" in both spaces). And, since the energy eigenstates of a free quantum field are discrete multiples of some basic quanta of momentum/energy, those quanta are called "particles". Do not confuse that concept with the classical concept of a spatially localized entity. Consider a guitar string vibrating back and forth. Now, imagine that the amplitude of the vibration can only take certain discrete values and that those values are integer multiples of some fundamental vibrational quanta (particle) called a "phonon". For example, let's say the amplitude was 9 times the fundamental amplitude. Physicists would say that 9 phonons ("particles" of vibration) are present. But, "where" are the particles of vibration? Kind of hard to answer that.

At the risk of muddying rather than clarifying the waters on this topic, I ask you to consider a concrete example of objective versus subjective in the realm of audio equipment reviews. If anyone here is familiar with the so-called "high-end audio" world, you'll understand immediately what I'm talking about. Essentially, there are two camps. The first, the objective reviewers, measure the performance of audio gear with sophisticated test equipment and review the equipment based on those objective (the measuring equipment is not prejudiced) measurements. Of course, these reviewers typically confirm the results with listening tests. The second camp, the subjectivist reviewers, review audio gear based on listening tests only. All pepper their "reviews" with vague terms that are in fact floating abstractions. According to the subjectivists, there are objectively unmeasurable differences in the performance of audio gear that their subjective sense of hearing unambiguously finds. Not surprisingly, these "golden eared" reviewers always loose this acute ability whenever (which is not often) they participate in rigorous double-blind listening tests, i.e., when possible sources of prejudice are removed. As an aside, the ludicrous claims of the high-end audiophiles and the amounts of money they gleefully spend on snake-oil products are well documented and make for some entertaining reading.

Food for thought... If there is in fact a metric expansion of space, entities can, in a certain sense, be "infinitely" far apart, i.e., they can become causally disconnected, unable to interact with each other by any possible means. Consider a couple of examples of how large distances are measured, e.g., RADAR or laser ranging of the moon. Over very large distances and in a metrically expanding space, there is the possibility that the radio or light wave never "catches up" with the receding entity. In effect, that entity is "infinitely" far away in the sense that no physical thing, even light, can ever get "there" from "here".

What if the universe were "shrinking" instead? Which case is more paradoxical?

I'm don't think that one can meaningfully talk about the extent of the universe unless it is qualified, e.g., the extent of the observable universe. Surely it's true that the distance between any two entities in the universe is finite and surely it's true that the extent of any entity is finite. I think, in this sense, it is correct to say that the universe is not infinite, i.e., that there are no infinite distances, infinite extents, etc. Nonetheless, there is no logical reason that distances and extents cannot be arbitrarily large, i.e., have no upper bound.

A circle is the one-dimensional boundary of the two-dimensional disk. The center of a circle is actually the center of the disk and is not in the circle. The circle has no boundary. As Wheeler famously said, "the boundary of a boundary is zero". IOW, the circle has no boundary because it is itself a boundary. If one were to consider only the 1-D space that is the circle, there is no center to speak of as there is no center in that space; the center is elsewhere. Similarly, the sphere is the 2-D boundary of the 3-D ball. The center of a sphere is actually the center of the ball and is not in the sphere...

Consider a sphere, the boundary of a ball, does the ball end at the boundary or does it begin at the boundary?

Compact Manifold A compact manifold is a manifold that is compact as a topological space. Examples are the circle (the only one-dimensional compact manifold) and the n-dimensional sphere and torus. Compact manifolds in two dimensions are completely classified by their orientation and the number of holes (genus). It should be noted that the term "compact manifold" often implies "manifold without boundary," which is the sense in which it is used here. When there is need for a separate term, a compact boundaryless manifold is called a closed manifold. That a circle, sphere, or torus is bounded is, as far as I can tell, not being questioned in this thread. That they are boundaryless evidently is. I hope that the above puts that misconception to rest. @Jake, It's clear that the center of a circle is not in the circle, right? And it's clear that it is special, i.e., unique, right? Thus, how can you say that any point in the manifold can be considered a center? Moreover, AFAIK, distance is a magnitude, i.e., positive (we're not talking about intervals here). Thus, the sum of the distances to all other points cannot be zero unless all "other" points are the chosen point.

I suspect from the above that you are failing to distinguish between the words "bounded" and "boundary". A thing can be both bounded and boundary-less. Consider a circle, an example of a closed curve. Where is the boundary? Where is the beginning of the curve? The end? Finiteness does not entail a boundary.

(1) Where is the center of the surface of the Earth? (2) If the universe has a boundary, what is it that is ending and what is it that's beginning?

is flawed. Finiteness doesn't entail a boundary. The surface area of a sphere is finite but that surface has no boundary and thus no center.

Have you established that the natural numbers form a set?

As trite as this sounds, I think what you need is a broader perspective to give you an appreciation for those things you have now that you take for granted. While you look for "stimulation", many, many others struggle merely for sustenance. Consider what these souls would think of your "predicament" and how many would gladly relieve you of it by trading places with you. This world can and, if you're not vigilant, will provide you with far more "stimulation" than you imagine. Be careful what you ask for.

I think that is spot on. Well put.